Chaos - James Gleick [146]
“Evolution is chaos with feedback,” Joseph Ford said. The universe is randomness and dissipation, yes. But randomness with direction can produce surprising complexity. And as Lorenz discovered so long ago, dissipation is an agent of order.
“God plays dice with the universe,” is Ford’s answer to Einstein’s famous question. “But they’re loaded dice. And the main objective of physics now is to find out by what rules were they loaded and how can we use them for our own ends.”
SUCH IDEAS HELP drive the collective enterprise of science forward. Still, no philosophy, no proof, no experiment ever seems quite enough to sway the individual researchers for whom science must first and always provide a way of working. In some laboratories, the traditional ways falter. Normal science goes astray, as Kuhn put it; a piece of equipment fails to meet expectations; “the profession can no longer evade anomalies.” For any one scientist the ideas of chaos could not prevail until the method of chaos became a necessity.
Every field had its own examples. In ecology, there was William M. Schaffer, who trained as the last student of Robert MacArthur, the dean of the field in the fifties and sixties. MacArthur built a conception of nature that gave a firm footing to the idea of natural balance. His models supposed that equilibriums would exist and that populations of plants and animals would remain close to them. To MacArthur, balance in nature had what could almost be called a moral quality—states of equilibrium in his models entailed the most efficient use of food resources, the least waste. Nature, if left alone, would be good.
Two decades later MacArthur’s last student found himself realizing that ecology based on a sense of equilibrium seems doomed to fail. The traditional models are betrayed by their linear bias. Nature is more complicated. Instead he sees chaos, “both exhilarating and a bit threatening.” Chaos may undermine ecology’s most enduring assumptions, he tells his colleagues. “What passes for fundamental concepts in ecology is as mist before the fury of the storm—in this case, a full, nonlinear storm.”
Schaffer is using strange attractors to explore the epidemiology of childhood diseases such as measles and chicken pox. He has collected data, first from New York City and Baltimore, then from Aberdeen, Scotland, and all England and Wales. He has made a dynamical model, resembling a damped, driven pendulum. The diseases are driven each year by the infectious spread among children returning to school, and damped by natural resistance. Schaffer’s model predicts strikingly different behavior for these diseases. Chicken pox should vary periodically. Measles should vary chaotically. As it happens, the data show exactly what Schaffer predicts. To a traditional epidemiologist the yearly variations in measles seemed inexplicable—random and noisy. Schaffer, using the techniques of phase-space reconstruction, shows that measles follow a strange attractor, with a fractal dimension of about 2.5.
Schaffer computed Lyapunov exponents and made Poincaré maps. “More to the point,” Schaffer said, “if you look at the pictures it jumps out at you, and you say, ‘My God, this is the same thing.’” Although the attractor is chaotic, some predictability becomes possible in light of the deterministic nature of the model. A year of